.. _sphx_glr_api_gallery_quantum_atoms_molecules:

Atoms and molecules
-------------------

Many-electron quantum mechanics by the self-consistent-field method:
Hartree-Fock energies of the hydrogen molecule and the helium atom, from
the minimal STO-3G basis to the Hartree-Fock limit.


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    <div class="sphx-glr-thumbcontainer" tooltip="Hartree (1928) let each electron move in the average field of all the others and iterated until the field reproduced itself. Fock and Slater (1930) added the exchange term required by the antisymmetry of the wavefunction. restricted_hartree_fock solves the resulting Roothaan equations FC = SC\varepsilon. This example follows the SCF iterations for helium, converges helium to the Hartree-Fock limit -2.86168 hartree with growing Gaussian bases, and traces the \mathrm H_2 bond, including the well-known failure of restricted Hartree-Fock at dissociation.">

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  :doc:`/api/gallery/quantum/atoms_molecules/plot_hartree_fock_self_consistent_field`

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      <div class="sphx-glr-thumbnail-title">Hartree-Fock: the self-consistent field for H₂ and helium</div>
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   /api/gallery/quantum/atoms_molecules/plot_hartree_fock_self_consistent_field